EXISTENCE RESULT FOR A CLASS OF N-LAPLACIAN EQUATIONS INVOLVING CRITICAL GROWTH

doi:10.1016/S0252-9602(17)30077-2

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (5): 1348-1360.doi: 10.1016/S0252-9602(17)30077-2

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EXISTENCE RESULT FOR A CLASS OF N-LAPLACIAN EQUATIONS INVOLVING CRITICAL GROWTH

Guoqing ZHANG¹, Weiguo ZHANG¹, Sanyang LIU²

1. College of Sciences, University of Shanghai for Science and Technology, Shanghai 200093, China;
2. College of Mathematics and Statistics, Xidian University, Xi'an 710071, China

Received:2016-02-29 Revised:2017-04-28 Online:2017-10-25 Published:2017-10-25
Supported by:
Supported by Shanghai Natural Science Foundation (15ZR1429500) and NNSF of China (11471215).

Abstract

Abstract:

In this paper,we consider a class of N-Laplacian equations involving critical growth

where Ω is a bounded domain with smooth boundary in RN (N > 2),f (x,u) is of critical growth.Based on the Trudinger-Moser inequality and a nonstandard linking theorem introduced by Degiovanni and Lancelotti,we prove the existence of a nontrivial solution for any λ > λ₁,λ_l=λ_l(l=2,3,…),and λ_l is the eigenvalues of the operator (-△_N,W₀^1,N(Ω)), which is defined by the Z₂-cohomological index.

Key words: nonstandard linking theorem, N-Laplacian equation, critical growth

Guoqing ZHANG, Weiguo ZHANG, Sanyang LIU. EXISTENCE RESULT FOR A CLASS OF N-LAPLACIAN EQUATIONS INVOLVING CRITICAL GROWTH[J].Acta mathematica scientia,Series B, 2017, 37(5): 1348-1360.

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EXISTENCE RESULT FOR A CLASS OF N-LAPLACIAN EQUATIONS INVOLVING CRITICAL GROWTH

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